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divisibility by prime numbers

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by bullshark » Thu Jun 18, 2009 3:31 pm
Not sure how to go about solving this one, (1) is easy to test but if a number is divisible by 4 different prime numbers, then that number cannot be a square???


If Q is a positive integer, is Q the square of an integer?
(1) Q is divisible by 4
(2) Q is divisible by exactly 4 different prime numbers





answer:


[spoiler](E) Statements (1) and (2) TOGETHER are NOT sufficient.[/spoiler]
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by dmateer25 » Thu Jun 18, 2009 3:42 pm
The number can be divisible by 2^2 * 3 * 5 * 7 and that is not a square.

However, if it was 2^2 * 3^2 * 5^2 * 7^2 then yes it would be a perfect square.

Looking at these two possibilities, they are both divisible by four and only 1 is a perfect square. Therefore, the answer is E.
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by bullshark » Thu Jun 18, 2009 3:46 pm
dmateer25 wrote:The number can be divisible by 2^2 * 3 * 5 * 7 and that is not a square.

However, if it was 2^2 * 3^2 * 5^2 * 7^2 then yes it would be a perfect square.

Looking at these two possibilities, they are both divisible by four and only 1 is a perfect square. Therefore, the answer is E.
Thanks. That makes sense.

however, I read the word "exactly" to mean that it was ONLY divisible by 4 prime numbers.

Is it true that if a number is ONLY divisible by 4 prime numbers, then that number cannot be a square?

Note to self: "exactly" does NOT mean "only"!!
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